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A248089
a(n) = Sum_{k=0..floor(n/4)} binomial(n-k, 3k)*(-3)^(3k)*4^(n-4k).
0
1, 4, 16, 64, 229, 592, -224, -18176, -175655, -1265732, -7914560, -44970752, -236014307, -1145932664, -5086940240, -19929220352, -61944816911, -81359219468, 858917862064, 10785877546432, 84667993188757, 555461238134080, 3268576565244544, 17688312222825472, 88631554966652233, 408731119650234796
OFFSET
0,2
LINKS
P. S. Bruckman and G. C. Greubel, Advanced Problem H-725, Fibonacci Quarterly, 52(2):187-190, 2014.
FORMULA
a(n) = (9n + 7 + 3^(3n/2)*(11*sqrt(2)*cos(n*arcsin(sqrt(2/27))) + sin(n*arcsin(sqrt(2/27))))/sqrt(2))/18.
G.f.: (1-4x)^2/((1-4x)^3+27x^4) = (1-4*x)^2/((x-1)^2*(1 - 10*x + 27*x^2)).
MAPLE
Gser:=series((1-4*x)^2/((1-4*x)^3+27*x^4), x = 0, 35): seq(coeff(Gser, x, n), n = 0 .. 30);
MATHEMATICA
LinearRecurrence[{12, -48, 64, -27}, {1, 4, 16, 64}, 30] (* Harvey P. Dale, Nov 21 2015 *)
CROSSREFS
Sequence in context: A189336 A262334 A065738 * A248088 A294037 A228735
KEYWORD
sign,easy
AUTHOR
Emeric Deutsch, Oct 27 2014
STATUS
approved